If a triangle has a 22 deg angle and a 46 deg angle, what can be established about the third angle measure and the type of triangle? (1 point)
112 ^ * The third angle measure is and the triangle is an acute triangle,
68 deg O The third angle measure is and the triangle is an obtuse triangle
112 deg The third angle measure is and the triangle is an obtuse triangle.
The third angle measure is 128 deg and the triangle is an obtuse triangle.
The third angle measure is 112 deg and the triangle is an obtuse triangle.
To determine the measure of the third angle and the type of triangle, you need to remember that the sum of the angles in a triangle is always 180 degrees.
Let's calculate the measure of the third angle:
Sum of angles in a triangle = 180 degrees
Given angles: 22 degrees, 46 degrees
Third angle = 180 degrees - (22 degrees + 46 degrees)
Third angle = 180 degrees - 68 degrees
Third angle = 112 degrees
Now, let's determine the type of triangle based on the angles:
Since the third angle measure is 112 degrees, this means that the triangle is an obtuse triangle.
Therefore, the correct answer is:
The third angle measure is 112 degrees, and the triangle is an obtuse triangle.
To find the measure of the third angle in a triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
In this case, you are given that one angle is 22 degrees and another angle is 46 degrees. To find the measure of the third angle, subtract the sum of these two angles from 180 degrees.
Third angle measure = 180 degrees - (22 degrees + 46 degrees)
Third angle measure = 180 degrees - 68 degrees
Third angle measure = 112 degrees
Now, let's determine the type of triangle based on the measure of the third angle.
An acute triangle is a triangle where all three angles are less than 90 degrees. In our case, the third angle measure is 112 degrees, which is greater than 90 degrees. Therefore, the triangle is not an acute triangle.
An obtuse triangle is a triangle where one angle is greater than 90 degrees. In our case, the third angle measure is 112 degrees, which is indeed greater than 90 degrees. Therefore, the triangle is an obtuse triangle.
Hence, the correct answer is: The third angle measure is 112 degrees and the triangle is an obtuse triangle.